PIPCFR: Pseudo-outcome Imputation with Post-treatment Variables for Individual Treatment Effect Estimation

Abstract

The estimation of individual treatment effects (ITE) focuses on predicting the outcome changes that result from a change in treatment. A fundamental challenge in observational data is that while we need to infer outcome differences under alternative treatments, we can only observe each individual's outcome under a single treatment. Existing approaches address this limitation either by training with inferred pseudo-outcomes or by creating matched instance pairs. However, recent work has largely overlooked the potential impact of post-treatment variables on the outcome. This oversight prevents existing methods from fully capturing outcome variability, resulting in increased variance in counterfactual predictions. This paper introduces Pseudo-outcome Imputation with Post-treatment Variables for Counterfactual Regression (PIPCFR), a novel approach that incorporates post-treatment variables to improve pseudo-outcome imputation. We analyze the challenges inherent in utilizing post-treatment variables and establish a novel theoretical bound for ITE risk that explicitly connects post-treatment variables to ITE estimation accuracy. Unlike existing methods that ignore these variables or impose restrictive assumptions, PIPCFR learns effective representations that preserve informative components while mitigating bias. Empirical evaluations on both real-world and simulated datasets demonstrate that PIPCFR achieves significantly lower ITE errors compared to existing methods.